Nonclassical dynamics of the methyl group in 1,1,1-triphenylethane. Evidence from powder 1H NMR spectra

Abstract

According to the damped quantum rotation (DQR) theory, hindered rotation of methyl groups, evidenced in nuclear magnetic resonance (NMR) line shapes, is a nonclassical process. It comprises a number of quantum-rate processes measured by two different quantum-rate constants. The classical jump model employing only one rate constant is reproduced if these quantum constants happen to be equal. The values of their ratio, or the nonclassicallity coefficient, determined hitherto from NMR spectra of single crystals and solutions range from about 1.20 to 1.30 in the latter case to above 5.0 in the former, with the value of 1 corresponding to the jump model. Presently, first systematic investigations of the DQR effects in wide-line NMR spectra of a powder sample are reported. For 1,1,1-triphenylethane deuterated in the aromatic positions, the relevant line-shape effects were monitored in the range 99-121 K. The values of the nonclassicality coefficient dropping from 2.7 to 1.7 were evaluated in line shape fits to the experimental powder spectra from the range 99-108 K. At these temperatures, the fits with the conventional line-shape model are visibly inferior to the DQR fits. Using a theoretical model reported earlier, a semiquantitative interpretation of the DQR parameters evaluated from the spectra is given. It is shown that the DQR effects as such can be detected in wide-line NMR spectra of powdered samples, which are relatively facile to measure. However, a fully quantitative picture of these effects can only be obtained from the much more demanding experiments on single crystals.

Linear absorption spectrum of a quantum two-dimensional rotator calculated using a rotationally invariant system-bath Hamiltonian

“…18,19 As an extension of the standard Brownian model, a periodic system-bath (PSB) model has been used in studies of inelastic nuclear scattering (NIS) and nuclear magnetic resonance (NMR). [20][21][22][23][24][25][26][27] This approach assumes that the system-bath interaction H I = V (θ)X(t) satisfies V (θ) = V (θ + 2π/N) for a C N symmetric rotator, where V (θ) is the system side of the system-bath interaction and X(t) is the collective coordinate of the bath, which corresponds to noise. While the quantum master equation derived from the PSB model can describe rotational bands, the overdamped peak predicted by this model is different from that which arises from the spectral collapse peak predicted by the classical Langevin approach.…”